Question

Test the conditional statement and its converse to determine whether the following biconditional is true. A number is divisible by 6 if and only if it is divisible by 3.

Answer 1

It is false because at least one part of the biconditional is false.

Explanation:

Answer 2

The bi-conditional is false.

Explanation:

We are told:

1. If a number is divisible by 6 then it is divisible by three, AND

2. If a number is divisible by 3 then it it divisible by six.

Both conditions must be true for the original bi-conditional statement to be true.

Statement 2 can easily be disproved by the counter example:

15 is divisible by 3 but is not divisible by six.

Which is why the given bi-conditional is FALSE.